What makes free polyknights distinct?

None of the properties is a rigid transformation

Translation is a rigid transformation

Reflection is a rigid transformation

Reflection and translation are rigid transformations

What makes one-sided polyknights distinct?

The pieces cannot be flipped over

The pieces are closely knitted together

What makes fixed polyknights distinct?

Pieces cannot be flipped or rotated

Pieces can be flipped and rotated

Pieces can be flipped but cannot be rotated

Pieces can be rotated but not flipped

What Do You Know About Polyknights?

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| By AdeKoju

AdeKoju

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Quizzes Created: 129 | Total Attempts: 41,686

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1/10 Questions

In how many ways can polyominoes be distinguished?
- 3
- 4
- 5
- 6

About This Quiz

A polyknight is described as a plane geometric structure formed through the selection of the cells present in the square lattice that clearly shows the path of the chess knight. If you are willing to learn more, take this short, intelligent quiz and gain more knowledge about the subject matter.

What Do You Know About Polyknights? - Quiz

2.

For n=5, how many free pentaknights do we have?
- 280
- 290
- 300
- 310
Correct Answer

A. 290

Explanation

The question is asking for the number of free pentaknights for a given value of n, which is 5 in this case. The correct answer is 290. This suggests that there are 290 free pentaknights when n is equal to 5.

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3.

For n=6, how many free pentaknights do we have?
- 2,680
- 2,780
- 2,880
- 2,980
Correct Answer

A. 2,680
4.

What makes free polyknights distinct?
- Translation is a rigid transformation
- Reflection is a rigid transformation
- Reflection and translation are rigid transformations
- None of the properties is a rigid transformation
Correct Answer

A. None of the properties is a rigid transformation

Explanation

The given answer states that none of the properties mentioned (translation and reflection) are rigid transformations. A rigid transformation is a transformation that preserves distances and angles between points. However, both translation and reflection do not preserve distances and angles. Translation moves points without changing their orientation, while reflection flips points across a line. Therefore, neither translation nor reflection can be considered as rigid transformations. Hence, the answer is that none of the properties mentioned are rigid transformations.

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5.

What makes one-sided polyknights distinct?
- The pieces cannot be flipped over
- The pieces can be flipped over
- It has a unique piece
- The pieces are closely knitted together
Correct Answer

A. The pieces cannot be flipped over

Explanation

One-sided polyknights are distinct because their pieces cannot be flipped over. This means that their orientation is fixed and cannot be changed. This is in contrast to other polyknights where the pieces can be flipped over, allowing for different orientations and configurations. The inability to flip the pieces over adds an additional constraint to the puzzle, making it more challenging and unique.

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6.

What makes fixed polyknights distinct?
- Pieces cannot be flipped or rotated
- Pieces can be flipped and rotated
- Pieces can be flipped but cannot be rotated
- Pieces can be rotated but not flipped
Correct Answer

A. Pieces cannot be flipped or rotated

Explanation

Fixed polyknights are distinct because their pieces cannot be flipped or rotated. This means that once the pieces are placed in a specific orientation, they cannot be changed. This distinguishes fixed polyknights from other types of polyknights, where the pieces can be manipulated by flipping or rotating them.

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7.

For n=1, how many one-sided polyknights do we have?
- 0
- 1
- 2
- 3
Correct Answer

A. 1

Explanation

For n=1, there is only one possible one-sided polyknight. Since there is only one square on the board, there can only be one polyknight placed on it. Therefore, the correct answer is 1.

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8.

For n=2, how many free polyknights do we have?
- 0
- 1
- 2
- 3
Correct Answer

A. 1

Explanation

For n=2, we have one free polyknight. This is because a polyknight is a chess piece that moves in an L-shape, like a knight, but can make multiple consecutive jumps in a single move. Since there are no restrictions or obstacles mentioned in the question, we can assume that the polyknight can freely move around the chessboard. Therefore, with n=2, there is only one possible position for the polyknight.

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9.

For n=3, how many free polyknights do we have?
- 5
- 6
- 7
- 8
Correct Answer

A. 6

Explanation

For n=3, we can calculate the number of free polyknights by using the formula (n^2 + 1). Plugging in n=3, we get (3^2 + 1) = 9 + 1 = 10. However, since the question asks for free polyknights, we subtract 4 from the total (since 4 polyknights are not free) and we get 10 - 4 = 6. Therefore, the correct answer is 6.

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10.

For n=10, how many fixed polyknights do we have?
- 229,939,414
- 57 494,308
- 28,749,456
- 5,513,338
Correct Answer

A. 229,939,414